Statistical properties of the spectrum of light pulses in fast pseudorandom word modulation of a single-mode semiconductor laser

Abstract

1 2 Abstract The spectrum of Single Mode Laser pulses generated by fast Pseudo Random Word Modulation is studied numerically for Return-to-Zero and Non-Return-to-Zero control signals. We analyze both statistics and the worst cases for the frequency chirp during each optical pulse, and we study the connection between these frequency chirps and the turnon times. We show that patterns in the modulation signal sequences contribute to chirp noise. The worst case values of the turn-on time and the chirp range are very similar in the two modulation schemes, hence, the optimum choice depends mainly on the characteristics of the decision circuit and on the driver and detector bandwidths.

Analysis of semiconductor laser dynamics under gigabit rate modulation

“…We define the turn-on delay as the time at which the power P 1 ͑t͒ in the 1 bit first surpasses 50% of the summation of the steady state powers corresponding to I b and I m , i.e., P 1 ͑t͒ crosses the middle of the eye diagram. Figure 6͑a͒ The calculated values of the TOJ around I b = I th are comparable to those calculated by Balle et al 8 In the high-biasing region, I b Ͼ 3.2I th , the TOJ saturates at about 2 ps regardless of the value of B. The magnitude of I b at which the turning to this slower rate happens increases with the increase of B; for example, it is I b Ϸ 1.4I th when B = 2.5 Gbits/ s, I b Ϸ 1.7I th when B = 5 Gbits/ s, I b Ϸ 2.5I th when B = 8 Gbits/ s, and I b Ϸ 3.2I th when B = 10 Gbits/ s. Since these turning currents are comparable to those deduced from Eq.…”

“…This factor is analogous to the Q factor that determines the BER in transmission systems. 25 We introduce numerical modeling of the optimum choice of the sampling and decision times for maximizing the Q signal and compare the results with those investigated by Balle et al 8 Dependences of the modulation characteristics on both the biasing and modulation currents as well as the bit rate are presented. We also assess the relative contributions of the laser intrinsic noise and pseudorandom bit pattern to the TOJ.…”

“…6,7 The TOJ comes from both the intrinsic intensity noise and the history of the bits preceding each 1 bit in the pseudorandom modulation pattern. The bitpattern-induced TOJ was proven as a main cause of chirp noise, 8 which gives a bit-error rate ͑BER͒ floor. 9 Gustavsson et al showed that the bit-pattern-induced TOJ is enhanced when the bit slot becomes shorter than the setting time of the relaxation oscillations.…”

“…They showed that the bit-pattern-induced TOJ is minimum when the laser is biased slightly under threshold. 8 However, such analysis was limited to injection currents near ͑under and above͒ threshold while fixing the modulation current at a higher value. Balle et al 8 also examined the dependence of the BER of the laser emission on the sampling time but at a fixed decision time demonstrating that the BER drops to lower values with the increase of the sampling time.…”

“…Balle et al 8 introduced statistical analysis of the spectral properties of laser pulses emitted under both return-to-zero ͑RZ͒ and NRZ modulation schemes with gigabit rates and investigated the TOJ and chirp noise. They showed that the bit-pattern-induced TOJ is minimum when the laser is biased slightly under threshold.…”